Big Damn Heroes Handbook is, functionally, a supplement. It can't stand alone as a ruleset.
It alters the advantages and disadvantages to be more like standard Cortex System, and expands the list. It provides options for tweaking the skill system. It provides some extra material on relationships, as well, giving them mechanical teeth.
Most of it is expansion, but the traits chapter is expansion and revision.
As for the Wikipedia entry, about it being the first iteration, Wikipedia is wrong. Serenity RPG is the second. Larry Elmore's Sovereign Stone is the first, and only later switched over to being a d20 product. But it's not labeled cortex as it was released by Weiss and Elmore DBA Sovereign Press well before Serenity RPG.